The step-taper active-region (STA) design concept is implemented for ~5.0 μm-emitting quantum cascade lasers (QCLs) grown by metal-organic chemical vapor deposition (MOCVD). Carrier-leakage suppression yields high characteristic temperatures for the threshold-current density Jth, T0, and for the slope efficiency ηsl, T1: 226 K and 653 K. Resonant-tunneling extraction from the lower level results in miniband-like extraction. In turn, the internal efficiency ηi is found, from a variable mirror-loss study, to be ~77%; thus approaching the ~90% upper limit, when employing only inelastic scattering. Considering interface-roughness and alloy-disorder scattering, the transition efficiency reaches values of ~95%. Then, the injection efficiency is ~81%, and, for λ = 4.6 μm, the wallplug-efficiency ηwp upper limit reaches 41.2%. Results include 4.2 W/A single-facet ηsl and 0.96 kA/cm2 Jth values. Buried-heterostructure (BH) QCLs provide single-facet 2.6 W continuous-wave (CW) power and 12% CW ηwp. Optimized 8 μm-emitting, STA-design QCLs provide 2 W/A ηsl, and 1.1 kA/cm2 Jth; and BH devices yield single-facet 1 W CW power and 6% CW ηwp.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
CorrectionsDan Botez, Jeremy D. Kirch, Colin Boyle, Kevin M. Oresick, Chris Sigler, Honghyuk Kim, Benjamin B. Knipfer, Jae Ha Ryu, Don Lindberg, Tom Earles, Luke J. Mawst, and Yuri V. Flores, "High-efficiency, high-power mid-infrared quantum cascade lasers [Invited]: erratum," Opt. Mater. Express 11, 1970-1970 (2021)
High-CW-power (i.e., watt-range), highly efficient mid-infrared (IR) (λ = 3-12 μm) quantum cascade lasers (QCLs) are needed for a wide range of applications, from remote sensing to infrared countermeasures. The internal (differential) efficiency ηi, as defined for interband-transition devices  and by us (per period) for QCLs [2–4], is a key factor in the external-differential-efficiency expression, since it encompasses all differential carrier-usage (i.e., the total injection efficiency, ηinj) and differential photon usage (i.e., the lasing-transition efficiency, ηtr ). For conventional QCLs the ηi values have been found to be rather low compared to theoretical upper limits of ~90% : only 50-60% in the 4.5-6.0 μm wavelength range [6,7] and only 57-67% in the 7-11 μm range [3,4] with, until recently, no clear explanation why that was the case. Consequently, our work has been aimed at bridging these gaps by identifying the causes of low internal efficiency, and then performing conduction-band engineering for substantially eliminating them. As a result, we combined [3,4] carrier-leakage suppression [8–14] with fast, miniband-like carrier extraction [3,4,11,13] such that ηi values have steadily increased and are now approaching their upper limit of ~90% for mid-IR QCLs (considering only inelastic scattering) . For instance, by stepwise tapering both the barrier heights and well depths in the active region (AR) (so-called step-taper active-region (STA) design ) in conjunction with fast, miniband-like extraction we have obtained  ηi values of ~86% at both λ = 8.4 μm and λ = 8.8 μm. We called those devices STA-RE-type QCLs, where RE stands for resonant extraction.
Here we present results of the implementation of the STA-RE device concept to 5.0 μm-emitting QCLs. Carrier-leakage suppression is evidenced by high characteristic temperature coefficients for the threshold-current density Jth, T0, and the slope efficiency ηsl, T1: 226 K and 653 K, respectively; for relatively low injector sheet-doping density (0.7 x 1011cm−2) 4.5-5.5 μm-emitting devices. (T0 is defined as: Jth(Tref + ΔT) = Jth(Tref) exp(ΔT/T0) and T1 defined as: ηsl(Tref + ΔT) = ηsl(Tref) exp(-ΔT/T1), where Tref + ΔT is the heatsink temperature and Tref is the reference heatsink temperature). The use of resonant-tunneling extraction from the lower laser level results in short lower-level global lifetimes  of ~0.19 ps. In turn, very high single-facet slope efficiencies (4.2 W/A) are obtained for 3 mm-long, HR-coated ridge-guide devices grown by MOCVD. An ηi value of ~77% is extracted, which is 30-50% higher than those obtained from conventional QCLs emitting in the 4-6 μm wavelength range. We also calculate the lifetimes and ηtr values while taking into account interface-roughness (IFR) scattering  and alloy-disorder (AD) scattering , and find an ~15% increase in the calculated ηtr value which, in turn, pushes the upper limit for ηi by ~5% in excess of 90%. Then the injection efficiency is found to be as high as 81%. CW data from buried-heterostucture (BH)-type devices: 2.6 W CW single-facet power and 12% CW single-facet wallplug efficiency ηwp, are some of the best results obtained for QCLs grown by MOCVD.
We also present results from optimized 8.0 μm-emitting STA-RE QCLs, consisting of increasing the dipole-matrix element and the number of periods to 45. High single-facet ηsl (2 W/A), single-facet ηwp (9%), and low Jth (1.1 kA/cm2) values are obtained from 3 mm-long, HR-coated ridge devices. Results include single-facet CW data from BH devices: 1.0 W maximum CW power and 6% maximum CW ηwp values, which are comparable to the highest reported single-facet CW results from 8.0 to 10.0 μm-emitting QCLs grown by either molecular-beam epitaxy (MBE) or MOCVD.
Finally, the upper-limit curve for the maximum wallplug efficiency ηwp,max of mid-IR QCLs is revised upwards to take into account 4.4-5.0 μm-emitting QCLs whose performance is enhanced via elastic scattering; in that, values ≥ 40% become possible at wavelengths ≤ 4.75 μm. We also discuss recently published calculations including elastic scattering, that yield very high wallplug-efficiency values for 4.6-7.8 μm-emitting QCLs; and add new experimental data points to the ηwp vs. wavelength plot.
Raising the wallplug efficiency of mid-IR QCLs to values ≥ 40% will drastically decrease the dissipated heat, thus benefitting a wide range of applications, especially the defense-related ones, since thermal-load management drives the packaged laser system’s size, weight and overall power consumption. Furthermore, since QCL degradation has been found to be primarily triggered by a thermal runaway process, and QCL self-heating is directly related to the wallplug-efficiency value , achieving wallplug efficiencies ≥ 40% will allow for long-term reliable QCL operation at multi-watt CW output powers; thus, paving the way for practical use of QCLs in many applications that require high CW powers, ranging from remote sensing to infrared countermeasures.
2. Internal-efficiency and injection-efficiency definitions for mid-IR QCL
The internal efficiency ηi is as a key factor in the external differential efficiency ηd expression for a QCL [3,4]:4] that ηi can be well approximated by the following:18–20] which reflects the degree of carrier leakage. Then, one can define a total injection efficiency:
The ηinj,tun term is generally close to unity, at threshold and at low drive levels above it. However, the ηp term, at threshold, can be significantly lower than unity at room temperature (RT) and especially above RT, due to two carrier-leakage mechanisms: (a) LO-phonon scattering from the upper laser level  and/or from (ground) states in the injector region ; (b) interface-roughness (IFR) scattering from the upper laser level  and/or from (ground) states in the injector region [20,21]. For tall-barrier devices the leakage constitutes carrier excitation to upper AR energy states [3,18] followed by relaxation to lower AR states; thus, a shunt-type leakage current. In general, ηp can be expressed as follows:15]:3,23]:3,23]; Γ is the optical-confinement factor to the core region; and g is the differential gain in the case of unity tunneling-injection efficiency and no carrier leakage, and can be obtained by using the expression for the gain cross-section gc  divided by Γ and multiplied by τup,g. Note that one can use the same expression for the injection efficiency for both the external differential efficiency and the threshold-current density [3,23,25] since the carrier leakage is proportional with the current density; thus, the pumping efficiency at threshold is the same as the differential pumping efficiency at and slightly above threshold . Because of this fact, (1) and (6) lead to ηd ≈αm[1 + αbf/(αm + αw)] (ηtr Np /Γg)(1/Jth). The values αm, αw, αbf, Γ, g and ηtr do not vary too much for QCLs emitting in the 3.5-5.5 µm range, especially for a fixed heat sink temperature, which leads to ηd ∝ 1/Jth. In [21, Fig. 3.6] we verified this relationship for a large number of mid-IR QCLs emitting in the 3.6-5.8 µm wavelength range.
3. Step-taper AR (STA) – resonant extraction (RE) 5 μm-emitting QCLs
3.1. Active-region design
The conduction-band diagram and relevant wavefunctions in the AR and extractor/injector regions are shown in Fig. 1 a), and relevant lower AR and extractor states are shown in Fig. 1(b). Just as for 8-9 μm-emitting STA-RE QCLs , the structure has been designed for both strong suppression of carrier leakage from the upper laser level, state 4, and resonant-tunneling extraction from the lower laser level, state 3. The barrier heights in the AR increase stepwise: x = 0.56, 0.63, and 0.93 in AlxIn1-xAs, and the well depths increase stepwise: x = 0.57, 0.60, 0.70 and 0.70 in InxGa1-xAs (i.e., the 3rd and 4th wells in Fig. 1(b) are deep wells, having lower-energy bottoms than wells in the injector region ). Due to asymmetry and Stark-shift reduction , the energy difference between the upper level and the next higher level, E54, increases to 98 meV and the lifetime τ54 reaches a value of 0.88 ps. These are relevant values for the leakage-current density, at threshold, from the upper level, Jleak,ul, which has been shown, for a four-QW AR, with E54 ≥ 50 meV, to be [18,26]:3]. In turn, at room temperature, the second part of the pumping-efficiency term in (4) increases from ~0.85  to ~0.99. Thus, a significant part of carrier leakage has been suppressed which resulted in high T0 and T1 values (next subsection). A similar effect occurs in so-called ‘shallow-well’ 4.9 μm-emitting QCLs  which we have shown  to, de facto, be a TA-RE-type QCLs. For those 3 QW-AR devices we calculate  E43 and τ43 values of ~79 meV and ~0.59 ps, at threshold, with injection into the upper level from the first excited state in the injector; that is, the so-called pocket-injector design .
As for lower-level(s) depopulation, we use a similar approach as previously employed for 8-9 μm-emitting STA-RE-type QCLs . That is, resonant-tunneling extraction from the lower laser level, state 3, which results in two lower laser levels: the AR state 3 and the extractor state 3′ [see Fig. 1(b)], coupled with resonant-tunneling extraction from an AR energy state or states below the lower laser levels. Additional AR low-energy states help with faster lower-levels’ depopulation. In this case levels 3 and 3′ have a splitting at resonance of 7.7 meV at a field of 71 kV/cm. State 2 is strongly coupled to state 2’: 12.3 meV splitting at ~58 kV/cm, and to state 2”: 15.1 meV at 74 kV/cm; thus both participate in resonant extraction out of the AR. States 1 and 1’ are weekly coupled to each other (4 meV splitting); thus, unlikely to lead to effective extraction, but help depopulate the lower laser levels. The global lifetimes for levels 3 and 3′ are 0.197 ps and 0.192 ps, respectively. Since near resonance the electrons are basically equally shared between levels 3 and 3′, the total lower-level lifetime, τ33’g, is the average of the global lifetimes ~0.194 ps; that is, similar to best values (~0.2 ps) for double-phonon-resonance (DPR) devices and lower than ~0.3 ps for nonresonant-extraction (NRE) devices . Therefore, we have miniband-like carrier extraction  as well as an improvement over the shallow-well QCL  which, due to only two lower AR states, has longer (~0.3 ps) lower-level lifetime . Since the “effective” global upper-state lifetime is calculated to be 0.96 ps, the transition efficiency becomes ~83%. This value is somewhat higher than those obtained from 8 to 9 μm-emitting STA-RE devices: 77-80%  and than typical values of ~78-80% for conventional 4.5-5.5 μm-emitting QCLs . For comparison, for the 4.9 μm-emitting TA-RE-like QCLs  we calculate an ηtr value of 86%. However, in subsection 3.3.2., where both IFR and AD scattering are considered, we find that the actual ηtr value is significantly higher in STA-RE devices than in TA-RE devices.
The QCL structures were grown via metal-organic chemical vapor deposition (MOCVD) with core-region layer thicknesses (in Å) for one period, starting right after the exit barrier, are: 26 , , , , 19 , 21, 17, 23, 16, 24, 15, 26, 15, 37, (10), 9, 41, (11), 36, (13), 31 , where normal script are In0.44Al0.56As barriers, bold italic script are In0.6Ga0.4As QWs, bold normal script are In0.7Ga0.3As QWs, italic script are In0.4Al0.6As barriers, bracketed italic script are In0.35Al0.65As barriers, italic script in parentheses are the tapered barriers within the active region: In0.37Al0.63As and In0.07Al0.93As, bracketed bold normal script are In0.68Ga0.32As QWs, bracketed bold italic script is an In0.64Ga0.36As QW, bold script in parentheses is an In0.57Ga0.43As QW, bracketed normal script is the In0.3Al0.7As exit barrier, and underlining indicates the doped layers. The AR was designed, via an eight-band k•p code initially used in , for emission at λ = 4.76 μm, and the dipole matrix element, considering transitions from the upper level 4 to both lower levels 3 and 3′, is 1.42 nm. Below a 40-period core, on a (1-2) x 1017-doped InP substrate, the following layers were grown: 2 μm-thick 2x1016-doped InP layer and a 0.1 μm-thick 5x1016cm−3-doped In0.53Ga0.47As layer. Above the core, the grown layers were: 0.1 μm-thick 5x1016cm−3-doped In0.53Ga0.47As layer, 2 μm-thick 2x1016cm−3-doped InP layer, 2.0 μm-thick 1017 cm−3-doped InP layer, 0.5 μm-thick 5x1018 cm−3-doped plasmon InP layer, and 0.15 μm-thick 2x1019 cm−3-doped InP cap layer. Devices were fabricated into ~23.5 μm-wide ridge guides, with current confinement via 400 nm-thick Si3N4, and with Ti/Au episide metallization. After wafer lapping and metallization, 3 mm-long bars were cleaved, high-reflectivity (HR)-coated on one facet and separated into chips.
3.3.1. Pulsed-operation characteristics
The lasers were driven at T = 20 °C with 200 ns pulses at 20 kHz repetition rate. The devices lased at ~5.0 µm. A longer emission wavelength relative to design was previously reported for MOCVD-grown QCLs  and attributed to interface compositional grading (not included in our code). A typical light vs. current-density curve is shown in Fig. 2(a) for a device of ~0.7x 1011cm−2 injector sheet-carrier density, ns. The Jth value is 0.96 kA/cm2 and Jmax is ~3.4 kA/cm2. The peak pulsed power is ~5.2 W and the slope efficiency is 4.2 W/A, which, to the best of our knowledge, is the highest single-facet value reported from 4.5 to 5.5 μm-emitting QCLs grown by MOCVD. These values correct for the 92% measurement efficiency of our test setup, which takes into account a 96% collection efficiency and a combined 96% transmission efficiency through two antireflection-coated lenses. The measurement setup consists of a calibrated thermopile and two high numerical-aperture, plano-convex lenses. The low Jth value reflects both a relatively vertical transition and, as we shall later see, a high (~81%) ηinj value. The T0 and T1 values: 226 K and 653 K, are high compared to values from low-doped (i.e., ns = 0.5-0.7 × 1011cm−2) conventional QCLs: ~200 K  and ~140 K , respectively; thus, reflecting, especially for the T1 value, that LO-phonon-assisted carrier leakage has been virtually suppressed. By comparison, for the low-doped TA-RE-type QCLs  T1 had a similar value (645 K) while To had a higher value: 383 K. However, this can be explained by the fact that for those devices, of same mirror loss, the Jth value was much higher than ours (~1.4 kA/cm2) in small part due to less core-region periods (30) and in large part due to the fact those devices involved a strong diagonal transition. If one adds the Jth difference at RT to our device’s Jth, the To value becomes similar to that in . For same-geometry (i.e., 3 mm-long, HR-coated) and heavier-doped (ns ≈1011cm−2) STA-RE QCLs the T0 and T1 values are found to be somewhat lower: 216 K and 400 K; thus, reflecting the influence of increased backfilling on T0, and of the increase in the intersubband (ISB) absorption part of the αw value on T1 . Higher-doped devices (ns ≈1.6 x1011cm−2) show similar trends: T0 = 197 K and T1 = 302 K; that is, still quite high T1 values thanks to efficient carrier-leakage suppression.
We show in Fig. 3 the inverse slope efficiency vs. inverse mirror loss for relatively low-doped STA-RE devices. A mirror-loss study, consisting of varying the front-facet reflectivity Rf of one STA-RE 3 mm-long, HR-coated ridge-guide chip, provided an ηi value of ~77% and a αw value of ~1.9 cm−1. The three data points correspond to three Rf values: 27% for the uncoated facet, and 45% and 60% values for e-beam evaporated coatings of alternating SiO2 and Ge films. By using the same chip we removed uncertainties when measuring different chips of different lengths and/or different facet coatings. 77% represents the highest ηi value reported to date from QCLs emitting in the 4.5-6.5 μm wavelength range, as can be clearly seen from Fig. 4. While conventional QCLs do provide ηi values in the 50-60% range [6,7], strong carrier-leakage suppression coupled with miniband-like extraction has resulted in ηi values at and above 70%: 70% from the so-called “shallow-well” device , which we have shown  to be a TA-type QCL, and 77% from our STA-RE QCL. A two-QW (2 QW)-AR NRE-type QCL , designed to have a large E54 value for carrier-leakage suppression, has resulted in a moderately-high value for ηi: ~62%; as extracted from the published 1/ηsl vs. cavity-length plot. This value is significantly lower than the 70-77% values for TA-RE and STA-RE-type QCLs, most likely due to a low ηtr value, as expected for NRE QCLs (e.g., an ~81% ηtr value is obtained from lifetimes calculated including elastic scattering  for ~4.6 μm-emitting NRE QCLs). In contrast to 8-9 μm-emitting QCLs, the highest ηi values of 4.5-5.0 μm-emitting QCLs are significantly below the upper limit of ~90%, when considering only inelastic scattering . The reason may well be relatively high IFR-mediated carrier leakage [20–22] in these high conduction-band (CB)-offset devices. However, with adequate IFR-scattering engineering we believe that ηi values well in excess of 80% are quite possible. We also show in Fig. 4, over the 4.0-5.5 μm wavelength range, an upper ηi limit of 95% based on results of calculations on STA-RE QCLs when considering elastic scattering (see next subsection).
3.3.2. The effect of elastic scattering on lifetimes and the lasing-transition efficiency
The analysis so far has been done considering only LO-phonon scattering of electrons. However, a realistic model has to take into account IFR scattering from interfaces [16,33] and AD scattering . Electron-electron scattering is absent in our analysis since it is negligible for mid-IR QCLs. We further neglect dopant-induced scattering since we analyze relatively low-doped devices. In any event, the latter is by and large negligible.
184.108.40.206. The effect of interface-roughness scattering
IFR scattering affects both the EL linewidth  and carrier lifetimes . First, one has to determine the structural parameters conventionally used in studying the effect of IFR on QCL performance: Δ, the average roughness height, and Λ, the average roughness correlation length along the interface plane, that characterize a standard Gaussian autocorrelation of the roughness [16,34]. The value of the ΔΛ product is extracted by comparing calculated electroluminescence (EL) spectra to experimentally obtained EL spectra. The FWHM values of the individual EL spectra correspond to the IFR-induced inhomogeneous broadening values between the involved levels, and are calculated as in [33,34]:Fig. 5) which reflects transitions from the upper laser level to both lower laser levels; that is, to states 3 and 3′.
In Fig. 6 we show how by using Eq. (8), with the contributions from transitions between levels 4 and 3, and 4 and 3′ being weighted by their respective oscillator strength, and a ΔΛ product is 1.207 nm2, we obtain a global FWHM EL value of 39.3 meV. The extracted ΔΛ value is ~30% higher than that typically considered average in IFR studies of QCLs (i.e., the ~0.9 nm2 value used in ), but it is close to a value of 1.08 nm2 reported by Vasanelli et al. . Note that the 4 to 3 transition has a FWHM of 32.9 meV; that is, quite similar to the 32.7 meV value reported by Lyakh et al.  for MOCVD-grown material with dipole matrix element z43 = 1.46 nm. However, this is just a coincidence since the lower z43 value in our case (i.e., 1.27 nm) is compensated for by the fact that the CB offsets for the first two AR barriers are smaller than for conventional QCLs (i.e., ~660 meV vs. ~800 meV). The scattering times for IFR-induced intersubband scattering between selected states of the old and new STA-RE QCL designs are calculated as in :Eq. (8) are used in the calculations of Eq. (9).
Since Eq. (9) contains the Λ parameter separate from the Δ parameter (i.e., in the argument of the exponential function), we can estimate it by an iterative process, given the experimental Jth value, and using the Jth expression in (6). As mentioned above, the value for the differential gain g can be calculated by using the expression for the gain cross-section gc  divided by Γ and multiplied by the global, effective upper-state lifetime τup,g which, in this case, is given by: (10)where τ33’g and τ43g are the lower- and upper-level global lifetimes when considering transitions from and to both lower laser levels (i.e., states 3 and 3′), respectively. One can easily calculate the gc value, given the EL FWHM, but τup,g can only be obtained by an iterative process, starting with the experimental Jth value: 0.96 kA/cm2. For the total injection efficiency ηinj, we know from calculations that ηinj,tun ≅ 97%, but we don’t know the ηp value. Then, as seen from Eq. (2), in order to obtain the ηinj value, one has to divide the experimentally determined internal efficiency ηi (i.e., 77% in this case) by the transition efficiency ηtr value when considering both inelastic and elastic scattering (i.e., including both IFR and AD scattering, to be addressed in the next subsection) Several iterations were performed that involved a parameter-sweep strategy consisting of sweeping both the Δ and Λ values, while tracking the global EL linewidth and Jth to stay within expected values of ~40 meV and ~1 kA/cm2, respectively. As a consequence, we found that Λ ≅ 10.5 nm. Then, Δ ≅ 0.115 nm, a value in good agreement with the 0.12 nm value considered in . We also note that the Λ value is close to the 10 nm value found to be optimal for lowest Jth and highest slope-efficiency values for 4.6 μm-emitting QCLs  of same z43 value (i.e., 1.27 nm)  as our QCL main transition. In the process, by using (9) and (11), from the next subsection, we obtained the elastic-scattering-induced lifetimes for all transitions. We show in Table 1 values for lifetimes caused by LO-phonon, IFR scattering, AD scattering and the total values.
Due primarily to AD scattering, the upper-state lifetime τ4g decreases from a 1.03 ps value to a value of 0.79 ps, since the transition mostly occurs on the left side of the AR where the first two barriers are relatively short. Similarly, the lifetime associated with the lasing transition, τ43g, decreases from 2.62 ps to 1.89 ps, primarily due to AD scattering. In sharp contrast, the decrease in lower-state lifetime from 0.19 ps to 0.04 ps is primarily due to IFR scattering, since the lower-level depopulation occurs on the right side of the AR where the barriers are tall, thus enhancing IFR scattering, while reducing AD scattering. (We have performed the same calculations for the so-called shallow-well structure , with Δ and Λ values used for MBE-grown structures (i.e., 0.1 nm and 9 nm, respectively), and obtained the same lifetime values as Faist reported  which gives us confidence that the above calculated lifetimes are accurate). The net effect is that the ηtr value increases from 83% to 95%, which means an ~15% increase in the maximum achievable wallplug-efficiency value. This significant increase in ηtr was expected since ηtr = τup,g/(τup,g + τ33’g) and, while the total τup,g decreases due to elastic scattering by only a factor of ~1.25, the lower-state lifetime τ33’g decreases by almost a factor of 5. (By contrast, for conventional 4-5 μm-emitting QCLs Chiu et al.  found that IFR-scattering rates are only 1.5- to 3-times larger than LO-photon scattering rates). This phenomenon happens since in STA-type active regions (see Fig. 1(a)) the conduction-band offsets, ΔCB, are much higher on the right side of the AR, where depopulation of the lower level primarily occurs, than on the left side of the AR where the lasing transition primarily occurs, and since the IFR-induced scattering rate is proportional with ΔCB2 [see Eq. (9)]. We note that increasing the ηtr value by introducing more IFR scattering on the right side of the AR has been previously proposed  for 8-9 μm-emitting conventional QCLs with a thin barrier inserted in the rightmost QW of the AR. In our case, however, there is no need for inserting additional barriers since by their very nature STA-RE active region ensure much taller barriers on the right side than on the left side of the AR. In turn, that allows for a much stronger effect of IFR scattering on the lower- than on the upper-level lifetime, which, when combined with the effect of AD scattering on the upper- and lower-level lifetimes, leads to significant increases in ηtr.
Now that we have a realistic value for ηtr and an experimental value for ηi, one can derive a realistic value for the ηinj value. We obtain ηinj ~81% which is, to the best of our knowledge, the highest injection-efficiency value reported for mid-IR QCLs. If we consider only LO-phonon-assisted carrier leakage, then ηp ~99% and, given a tunneling-injection efficiency of ~97% and the elastic-scattering enhanced ηtr value (95%), by using Eq. (2) the expected ηi value is ~91%. That is, the expected ηi value is 18% higher than the measured value (i.e., 77%); a fact we call an 18% “gap“. Similarly, for the TA-RE-like 4.9 μm-emitting QCL, by using the reported ηi value: 70%  and a total transition efficiency of ~ 88%, derived from τup,g and τ2g values computed including elastic scattering (see next subsection and ), the estimated ηinj value is ~ 80%, and there is also an ~ 18% gap between experimental value and the calculated ηi value of ~ 83% (when considering only inelastic-scattering carrier leakage) . We believe that this 18% gap, for both STA-RE and TA-RE 4.9-5.0 μm-emitting QCLs, mostly reflects IFR-mediated carrier leakage, to the next higher AR energy state(s), from the upper laser level  and possibly from states in the injector region as well [20,21].
Finally, the fact that lower-level depopulation is dominated by IFR scattering means that LO-phonon scattering becomes basically irrelevant for lower-level depopulation. Then, due to IFR scattering, the carrier extraction involves both coherent and incoherent resonant tunneling, just like IFR scattering causes (resonant) injection from the injector ground state into the upper laser level to be partly coherent and partly incoherent tunneling . The very fast IFR-caused lower-level depopulation may explain why we find that αbf is only ~0.4 cm−1; that is, the so-called transparency current (i.e., Jbf,th/ηp) is only ~9% of the Jth value. In other words, due to much faster lower-level depopulation than in the case of LO-phonon-only scattering, conventional ways for calculating the backfilling current may not apply.
220.127.116.11. The effect of alloy-disorder scattering and comparison to TA-RE QCLs
AD scattering does not affect the EL linewidth, but it impacts carrier lifetimes, especially for QCLs involving lattice-matched superlattices, when it can account for as much as 70% of the elastic scattering . The scattering times for AD-induced intersubband scattering between selected states are given by :Table 1. Note that for x = 0.5 one obtains the shortest lifetimes. This is why for lattice-matched structures (i.e., when x is very close to 0.5) the effect of AD scattering is strongest ; that is, for conventional 8-16 μm-emitting QCLs. Similarly the effect of AD scattering strongly impacts the upper-state lifetimes in TA-type ARs such as in the case of the so-called shallow-well (i.e., TA-RE) QCL  for which the first well and barrier in the AR are lattice-matched. We have calculated that structure with the Δ and Λ values we extracted for our structure (i.e., 0.115 nm and 10.5 nm) and find the following: (a) the upper-state lifetime τ3g is dominated by AD scattering and decreases to 0.49 ps: a factor of ~4 times lower than the inelastic-scattering value; (b) the lower-state lifetime τ22’g is primarily affected by IFR scattering and decreases to 0.05 ps: a factor of ~6 times lower than the inelastic-scattering value; and (c) the ηtr value increases to 90%; that is, only 5% higher than the inelastic-scattering value (86%) and thus a factor of 3 lower ηtr enhancement than in STA-RE QCLs. We also find, just as for STA-RE QCLs, that the transparency-current density is only ~10% of the Jth value, thus indicating negligible backfilling due to very fast lower-level depopulation via IFR scattering.
The enhancement in ηtr for TA-RE QCLs is much less pronounced when considering Δ and Λ values used for MBE-grown structures (i.e., 0.1 nm and 9 nm), in that ηtr is 88% ; thus, only an ~2% ηtr enhancement is obtained. Therefore, in shallow-well QCLs the effect of AD scattering on the upper-level lifetime is compensated for by the effect of IFR scattering on the lower-level lifetime, to the effect that the ηtr value is basically unaffected by elastic scattering. Of course, if the Δ and Λ values are lowered to the MBE ones for STA-RE QCLs, the ηtr enhancement will be lower than 15%, but we expect that the effect on the maximum wallplug efficiency will be negligible due to lowering of the Jth value as a result of a significant decrease in the EL-spectrum FWHM value; i.e., ηwp values ≥ 40% should still be possible.
3.3.3. CW-operation characteristics
Low-injector-doped (ns ≈0.7 × 1011cm−2) material was processed into BH-type devices. 4.5 mm-long BH devices of 10.6 μm-wide buried ridges were HR-coated and 14% front-facet-coated using an Y2O3 film, and mounted on diamond submounts using indium solder. We obtained up to 2.6 W CW single-facet power, at a temperature of 15 °C (Fig. 7), which is, to best of our knowledge, the highest published CW single-facet power from MOCVD-grown QCLs. Compared to MBE-grown QCLs, also mounted on diamond submounts [32,35], this is a lower value for one main reason: the αw value, which likely is ~1.5 cm−1 (given that for ridge-guide devices it is ~1.9 cm−1 (Fig. 3)), is significantly higher than that for optimized MBE-grown 40-period devices (~0.5 cm−1) [6,32]. Nonetheless, the 2.6 W CW single-facet value is not much different from the 3 W CW value obtained from MBE-grown NRE devices of similar geometry. We attribute this coincidence to the fact that the NRE QCLs have been found to have an ηi value of ≈50%  while the STA-RE devices have an ηi value of ≈77%, due to both carrier-leakage suppression and fast, miniband-like carrier extraction, primarily due to IFR-induced intersubband scattering. The CW wallplug efficiency ηwp reaches a maximum single-facet value of 12% (Fig. 7). This is a very high value for MOCVD-grown devices; and relatively high considering that the αw value is, as mentioned above, likely to be ~1.5 cm−1 as opposed to ~0.5 cm−1 values for MBE-grown devices. (Similarly, the maximum pulsed ηwp value: 14%, is high for MOCVD-grown devices, but significantly lower than theoretical expectations , primarily due to the high αw value). Again, comparing to NRE-type devices of similar geometry mounted on diamond submounts , but of significantly lower ηi value, the maximum CW ηwp value is similar (i.e., 12% vs. 12.4%). Still the value is significantly smaller that for heavier doped, TA-RE-type QCLs  (i.e., 21%) with αw ~0.5 cm−1 and having carrier-leakage suppression as well as miniband-like carrier extraction. We believe that upon MOCVD crystal-growth optimization, for minimizing the αw value close to ~0.5 cm−1, CW wallplug-efficiency values well in excess of 20% are definitely possible.
4. STA-RE-type, 8-9 μm-emitting QCLs
We have previously reported on 8.8 μm-emitting, low-doped (~0.7x1011 cm−2) STA-RE QCLs  as well as 8.4 μm-emitting, moderately-high-doped (~1.65x1011) STA-RE QCLs . Both devices had 35-period core regions. Due to significant carrier-leakage suppression, both devices displayed much higher T0 and T1 values than conventional 8-9 μm-emitting QCLs of similar injector-doping level. High ηtr values: ~77% and ~71.5%, respectively; calculated while considering only LO-phonon scattering, reflected fast, miniband-like extraction. In turn, high slope-efficiency, ηsl/period values were obtained. For instance, 8.8 μm-emitting devices displayed a 35 mW/A ηsl/period value; i.e., ~40% higher than for same-geometry conventional 8-9 μm-emitting QCLs . Variable mirror-loss studies revealed, for both 8.4 μm- and 8.8 μm-emitting, same-structure devices, the same high internal efficiency ηi value: ~86%. We show in Fig. 8(a) results from 8.8 μm-emitting QCLs. Although data from different uncoated and HR-coated devices were employed, from four devices of same cavity length, the fact that both pairs of uncoated and back-facet HR-coated devices have virtually identical slopes [i.e., the two pairs of overlapping data points in Fig, 8 (a)] provides validity to the extracted ηi value. Further confidence that the extracted ηi values are highly accurate comes from the fact that the extracted αw values, in both cases, agree very well (i.e., within 5%) with values derived from conventional 8-9 μm-emitting, 35-period QCLs .
Figure 8(b) shows a comparison of internal efficiencies from different QCL types emitting in the 6.5-11.5 μm range. The STA-RE data points are 30-50% higher than conventional QCLs because they combine carrier-leakage suppression with miniband-like extraction. The best result from conventional QCLs (i.e., the 67% value derived in  from published data in [5, 39]) was obtained from a DPR-like device that, according to our calculations and the CB diagram in , had resonant extraction from the lower laser level and, in turn, miniband-like extraction. Being the highest experimentally obtained ηi value at the time (i.e., 2007), the ~67% value was used for deriving the upper limits in ηwp for mid-IR QCLs  (see the black curve in Fig. 12). With the realization of much higher ηi values from STA-RE devices, and given the fact that the upper ηi limit is ~90% (when only LO-phonon scattering is considered) we drew a curve for the upper limit in ηwp for mid-IR QCLs . However, that curve did not take into account elastic scattering, which, as we shall see below, allows for even higher ηwp upper limits than previously predicted.
4.2. 8 μm-emitting, 45-period QCLs
4.2.1. Pulsed-operation characteristics
STA-RE-type QCL structures of basically the same AR design as in  were grown by MOCVD. The AR was designed for emission at λ = 7.79 μm, with the same E54 and τ54 values as in  (i.e., ~74 meV and ~0.65 ps, respectively), lower voltage defect at resonance Δinj,res (175 meV vs. 212 meV), and higher dipole-matrix element z43 (21.2 Å vs. 19.7 Å). However, the increased z43 value resulted in a lower τup,g value (i.e., 0.68 ps vs. 0.88 ps),which, in turn, led to the calculated ηtr value to significantly decrease; i.e., from ~77% to ~71.5%. The core region was grown with 45 periods, in order to reduce the αw value. In addition, the thickness of the InGaAs light-confinement layers on either side of the core region was reduced from 0.2 μm to 0.1 μm, and the second upper-cladding layer (1017 cm−3-doped) was reduced from 2 μm to 1.5 μm.
Pulsed-drive L-I-V curves and the ηwp curve, for 3 mm-long, HR-coated devices, are shown in Fig. 9. Although the target injector sheet-doping density ns was 1011 cm−2, we obtained a Jmax value of only ~3.5 kA/cm2; thus, indicating an actual ns value of ~0.7x1011 cm−2. Then, the best comparison is to the low-doped 8.8 μm-emitting STA-RE QCLs . The room-temperature Jth value dropped from ~1.58 kA/cm2 to ~1.1 kA/cm2. This significant drop reflects the following: (a) unlike the device in , there is no “bottleneck” at and slightly above threshold; (b) the increased stage number raises the Γ value; (c) a decrease in the αw value; and (d) a higher z43 value. The single-facet slope efficiency value (2 W/A) is quite high for 8 μm-emitting QCLs. The ηsl/period value: 44 mW/A is significantly higher that that obtained from similarly low-doped 8.8 μm-emitting STA-RE QCLs (i.e., 35 mW/A); thus, ~80% higher than for conventional 8-9 μm-emitting QCLs of similar doping level. The large increase in the ηsl/period value also indicates a significant decrease in the αw value. The maximum ηwp value is 9%, the highest single-facet value for 8 μm-emitting QCLs. In fact, considering uncoated facets, it translates to 13%, a value higher than all such values reported for 8-11 μm-emitting QCLs with the notable exception a heavily-strained, 9 μm-emitting QCL  well-known for having a low αw value because of very low intersubband-absorption loss αISB. In order to compare the maximum ηwp value to those from the previously reported STA-RE devices emitting at 8.8 μm  (i.e., ~3.9%) and 8.4 μm  (i.e., ~5.5%) we use the ηwp,max equation from  to which we add a factor for the pulsed L-I deviation from linearity at the ηwp,max point, ηs :
We performed a similar variable mirror-loss study as shown in Fig. 8(a) and found that ηi ~80% and αw ~3.5 cm−1. The former reflects the smaller calculated ηtr value for this design compared to that for 8.4 μm-emitting STA-RE devices (i.e., ~71.5% vs. ~77%). Given that the devices have similar tunneling-injection efficiency (~97%) and the same negligible degree of carrier leakage, due to same high E54 and τ54 values, as evidenced by very similar high T1 values, it is reasonable to assume that the ratio of the measured ηi values reflects quite accurately the ratio of the calculated ηtr values. Since for the 8.4 μm-emitting devices we obtained ηi ~86%, it follows that for the 8 μm-emitting devices ηi ~80%.; thus, there is a good agreement with the experimental value. However, as discussed for 5 μm-emitting STA-RE devices (section 18.104.22.168), the ηi value when considering elastic scattering is likely to be significantly higher than that computed using only LO-phonon scattering. For instance, Chiu et al.  have shown that ~7 μm-emitting QCLs can be IFR-engineered to obtain low lower-level lifetimes, such that the ηtr value can be increased by 62%, though the inelastic ηtr value was relatively low (47%) to start with. More recently, by considering elastic scattering and using the pocket-injector design, Wolf  predicted ηtr values of 87% and 83% for lattice-matched, 7.2 μm-emitting and strained-layer, 7.8 μm-emitting QCLs, respectively.
As for the estimated αw value, it can be justified as such: Our calculated loss outside the core region is 1.8 cm−1 in good agreement with a value of 2.1 cm−1 for QCLs emitting at 8.2 μm  and of virtually identical Γ value (74% vs. 73% in our case). As for the loss in the core it is dominated by intersubband absorption, αISB. From the same reference, at 8.2 μm wavelength, the ΓαISB value is ~2.7 cm−1. However, those devices had an injector sheet-doping density twice higher than our devices; thus, since intersubband absorption (for non- heavily strained devices) is basically proportional with the doping level, we estimate an ΓαISB value of ~1.35 cm−1 for our devices, which gives a calculated αw value of 3.25 cm−1. Further proof that the estimated ηi· and αw value are quite accurate comes from the fact that by using them we were able to justify above the difference in ηwp values between 8.0 μm STA-RE QCLs and 8.4 μm and 8.8 μm STA-RE QCLs; and, as shown below, between 8.0 μm STA-RE QCLs and the 9.0 μm-emitting NRE-type heavily-strained QCL of . Heavily-strained ~9.0 μm-emitting NRE QCLs  have provided a low αw value (1.6 cm−1), apparently due to much lower ISB-absorption loss. However, those devices had a low ηi value (~58%) [3,4], most likely due to moderately-high carrier leakage, since the E54 value was relatively low (60 meV) and the high Jth value (2.1 kA/cm2) likely led to a high electronic temperature in the upper laser level . Nonetheless, those devices provided a record-high both-facets ηwp value (i.e., 16%) for 8-11 μm-emitting QCLs. The difference in ηwp between the one in this paper (9%, single facet) and the both-facets value obtained in  can be justified by using Eq. (12) with values extracted from Fig. 9, and from Figs. 3 and 4(a) in . While the 9 μm heavily-strained NRE QCL has a significantly lower internal efficiency than the 8 μm STA-RE QCL (i.e., ~58% vs. ~80%), that is more than offset by an almost twice as high value for the αm /(αm + αw) quantity. This large difference is, on the one hand, due to uncoated facets, since that basically doubles the αm value (i.e., 4.36 cm−1 vs. 2.2 cm−1) and, on the other hand, due to much lower αw value (1.6 cm−1 vs. 3.5 cm−1) which reflects very low ΓαISB values (~0.5 cm−1).
We conclude that by using strained-layer, 8 μm-emitting devices together with inherently high-ηi QCL structures, via carrier-leakage suppression and miniband-type extraction, as well as with IFR- and/or AD-scattering engineering, very high ηwp,max values, close to predictions including elastic scattering  (see subsection 5), can definitely be achieved.
Material was processed in BH-type devices which had HR-coated back facets and 6 mm-long cavity. We show in Fig. 10 the threshold-current and slope-efficiency variations with heatsink temperature, over the 10-100 °C heatsink-temperature range, for 6 mm-long and 11 μm-wide buried-ridge devices. The high T0 and T1 values: 228 K and 529 K, respectively, over a large temperature range, attest not only to strong carrier-leakage suppression, but also to effective current blocking by the Fe-doped semi-insulating layers regrown around the buried ridge. The T0 is only slightly higher than that in similar injector-doping 8 μm-emitting QCLs (i.e., 215 K in ), but occurs for significantly lower initial Jth values (i.e., ~1 kA/cm2 vs. ~1.5 kA/cm2). The T1 value, the primary indicator of carrier leakage, is quite similar to that obtained from the low-doped 8.8 μm-emitting STA-RE QCLs  (~550 K) and basically twice those from conventional 8.0-8.4 μm-emitting QCLs (i.e., 260 K [3,33] and 236 K ).
4.2.2. CW-operation characteristics
The BH devices were mounted episide-down with In solder on Cu submounts which were screwed into a water cooling block without Peltier element. We obtained up to 1 W CW single-facet power, at a heatsink temperature of 14 °C (Fig. 11) which is the same value as the highest single-facet CW powers reported from devices emitting in the 8-10 μm wavelength range . The maximum achieved single-facet CW wallplug efficiency is 6%, which, to the best of our knowledge, is the highest single-facet CW value reported to date from 8.0 μm-emitting QCLs.
5. Fundamental limits for the wallplug efficiency revisited
In a previous publication  we showed what happens to the original upper limits for mid-IR QCL wallplug efficiency ηwp,max , derived considering the best ηi value at the time (i.e., ~67%), when taking an upper-limit ηi value of ~90%. The latter was obtained by considering an ideal case when the lasing transition occurs via relaxation to the top of a miniband, instead to a discrete energy state, thus, providing very short (~0.1 ps) lower-level lifetimes , and a generic 1.0 ps effective upper-state lifetime (i.e., ηtr ~90%), no carrier leakage, and 100% tunneling-injection efficiency (i.e., a total injection efficiency of 100%). With IFR scattering taken into account we find that for STA-RE QCLs, designed for 4.76 μm emission, the ηtr value increases from ~83% to ~94.7%, due to much stronger effect of the IFR scattering on the lower-level lifetime than on the effective upper-state lifetime. We have also designed a STA-RE QCL for emission at λ = 4.39 μm, and find that a similar effect occurs: the ηtr value increases from ~83% to ~95.4%. Therefore, we drew an upper-limit ηwp,max curve between 4.0 μm and 5.5 μm wavelengths (see the red dashed curve in Fig. 12) corresponding to ηi ≈95%, since the various design parameters should not change very much over that wavelength range. Then, the ηwp,max upper limit is at or above 40% for λ ≤ 4.75 μm, and reaches values of 41.2% and 45% for λ = 4.6 μm and λ = 4.0 μm, respectively. We note that Wolf , by using the so-called genetic design and employing a pocket-injector-type QCL , calculates a ηwp,max value of 44% for λ = 4.6 μm, while using a device of very large dynamic range and a voltage “defect” at threshold of only 83 meV. Then, it is fair to assume that the voltage “defect” at resonance Δinj,res is likely in the 115-120 meV range. Given that, as shown above, for STA-RE devices the very fast IFR-scattering-induced lower-level depopulation results in relatively little backfilling, STA-RE devices of Δinj,res ~120 meV may well be practical. In turn, by employing the ηwp,max approximation formula [4,5] with 120 meV for Δinj,res rather than the 150 meV value used in Fig. 12, the ηwp,max upper limit for λ = 4.6 μm increases from ~41.2% to ~44.4%; that is, basically the same value predicted by Wolf . Note that in Fig. 11 we have added four data points to those already reported in : this work’s single-facet values at λ = 5 μm and λ = 8 μm, and the 12% and 8% both-facets values recently reported by Schwarz et al.  at λ = 8 μm and by Wang et al.  at λ = 9.3 μm, respectively. The black solid curve corresponds to the original predicted ηwp,max vs. λ curve , for which ηi was taken to be 67%. Three data points agree very well with that curve, simply because they had ηi values close to 67% . The data points indicated by empty circles correspond to devices of both facets uncoated. As pointed out before , this significantly enhances the pulsed ηwp values, but at a price in large Jth values which, for some of the highest ηwp data shown in the figure (e.g., 18.9% at λ = 7.1 μm and 16% at λ ≈9.1 μm), severely impaired the devices CW performance; and, for that matter, for the device of highest ηwp value (i.e., 28.3% at λ ≈5.6 μm) did not allow CW operation.
At longer wavelengths the effect of elastic scattering on lifetimes dramatically increases  although the CB offsets by and large decrease. Wolf  predicts an ηwp,max value of ~35% for λ = 7.1 μm, while making sure that the Jth value is small enough (~1.3 kA/cm2) for reasonably-high efficient CW operation, and still taking a large dynamic range (Jmax /Jth ~9). The calculated value is significantly higher than the one predicted for λ = 7.1 μm when only LO-phonon scattering is considered (i.e., 25%, on the red solid curve in Fig. 11). Then, for a lattice-matched 8.7 μm-emitting device Wolf  predicts a ηwp,max value of ~27%, for a relatively high Jth value (1.55 kA/cm2). Finally, for a strained-AR, ~7.8 μm-emitting device Wolf predicts a ηwp,max value of ~37%, again for a relatively high Jth value (1.7 kA/cm2). The latter two values may be impractical for high CW wallplug-efficiency operation, since the Jth value directly impacts the core-temperature rise . For instance, for the TA-RE QCL  (pocket-injector-type injection) which had Jth,CW ~1.4 kA/cm2 and a relatively high thermal resistance , while the single-facet pulsed ηwp,max was 27%, the CW ηwp,max value was only 21%. We did show that at the CW ηwp,max point the core-temperature rise was quite high: ~53 K ; thus, not at all conducive to long-term reliability. Nonetheless, Wolf’s work confirms that, at least over the 4.6-8.7 μm wavelength range, when elastic scattering is taken into account, the ηwp,max values are likely to be much higher than when only LO-phonon scattering is considered.
In conclusion, by combining carrier-leakage suppression with fast, miniband-like extraction we have realized 5 µm-emitting QCLs of record-high internal (77%) and injection (81%) efficiency values. Taking into account interface-roughness (IFR) scattering, we find that for STA-RE-type QCLs, the transition efficiency is enhanced by ~15% at both 4.4 µm and 4.76 µm wavelengths, which, in turn, results in wallplug-efficiency upper limits larger than 40% for emission wavelengths ≤ 4.75 µm. For a voltage defect at resonance of 120 meV the wallplug-efficiency upper limit at 4.6 µm wavelength increases from 41.2% to 44.4%. Then, an ~40% CW wallplug-efficiency upper limit becomes possible. An ~18% gap is found between experimental and theoretical internal-efficiency values of 4.5-5.0 µm-emitting QCLs, which we suggest is primarily due to IFR-mediated carrier leakage.
In CW operation 5 µm-emitting devices reach 2.6 W single-facet power and 12% single-facet wallplug efficiency, some of the best results achieved to date from MOCVD-grown QCLs. Optimized 8 µm-emitting STA-RE QCLs provide 1.0 CW single-facet power and 6% CW single-facet wallplug efficiency, which are basically the same as the best results reported to date from 8 to 9 µm-emitting QCLs.
The realization of QCL material with CW wallplug efficiencies ≥ 40% will not only have a strong positive impact on the performance of single-element QCLs, but also prove to be the key to high-power quasi-CW or CW operation from large-aperture (>100 μm) spatially coherent devices such as resonant leaky-wave coupled  phase-locked QCL arrays , just as high wallplug-efficiency diode-laser material led to watt-range CW phase-locked laser arrays .
US Army (W911NF-12-C-0033); US Air Force Research Laboratory (FA8650-13-2-1616); US Navy (N68335-17-C-0466).
The authors gratefully acknowledge valuable discussion with Alexey Belyanin, Sushil Kumar and Angela Vasanelli as well as research support thanks to a gift contribution by Northrop Grumman.
References and links
1. P. M. Smowton and P. Blood, “The differential efficiency of quantum well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 491–498 (1997). [CrossRef]
2. D. Botez, J. Shin, S. Kumar, L. J. Mawst, I. Vurgaftman, and J. R. Meyer, “Electron leakage and its suppression via deep-well structures in 4.5–5.0 μm-emitting quantum cascade lasers,” Opt. Eng. 49(11), 111108 (2010). [CrossRef]
3. D. Botez, C.-C. Chang, and L. J. Mawst, “Temperature sensitivity of the electro-optical characteristics for mid-infrared (λ = 3–16 μm)-emitting quantum cascade lasers,” J. Phys. D Appl. Phys. 49(4), 043001 (2016). [CrossRef]
4. J. D. Kirch, C.-C. Chang, C. Boyle, L. J. Mawst, D. Lindberg, T. Earles, and D. Botez, “86% internal differential efficiency from 8 to 9 µm-emitting, step-taper active-region quantum cascade lasers,” Opt. Express 24(21), 24483–24494 (2016). [CrossRef] [PubMed]
5. J. Faist, Appl. Phys. Lett. “Wallplug efficiency of quantum cascade lasers: critical parameters and fundamental limits,” 90, 253512 (2007).
6. R. Maulini, A. Lyakh, A. Tsekoun, R. Go, C. Pflügl, L. Diehl, F. Capasso, and C. K. N. Patel, “High power thermoelectrically cooled and uncooled quantum cascade lasers with optimized reflectivity facet coatings,” Appl. Phys. Lett. 95(15), 151112 (2009). [CrossRef]
7. Y. Bai, S. Slivken, S. R. Darvish, and M. Razeghi, “Very high wall plug efficiency of quantum cascade lasers,” Proc. SPIE 7608, 76080F (2010). [CrossRef]
8. J. C. Shin, M. D’Souza, Z. Liu, J. Kirch, L. J. Mawst, D Botez, I Vurgaftman, and J. R. Meyer, “Highly temperature insensitive, deep-well 4.8 µm emitting quantum cascade semiconductor lasers,” Appl. Phys. Lett. 94, 201103 (2009). [CrossRef]
9. J. C. Shin, “Tapered active-region quantum cascade laser” in [Very low temperature sensitive, deep-well quantum cascade lasers (λ = 4.8 μm) grown by MOCVD], PhD Thesis, University of Wisconsin-Madison, 92–103, (2010) http://digital.library.wisc.edu/1793/52493
10. D. Botez and J. C. Shin, US Patent 8,325,774 B2 (2012) (www.google.co.in/patents/US8325774A).
11. Y. Bai, N. Bandyopadhyay, S. Tsao, E. Selcuk, S. Slivken, and M. Razeghi, “Highly temperature insensitive quantum cascade lasers,” Appl. Phys. Lett. 97(25), 251104 (2010). [CrossRef]
12. J. D. Kirch, J. C. Shin, C.-C. Chang, L. J. Mawst, D. Botez, and T. Earles, “Tapered active-region quantum cascade lasers (λ = 4.8 μm) for virtual suppression of carrier-leakage currents,” Electron. Lett. 48(4), 234 (2012). [CrossRef]
13. J. D. Kirch, C.-C. Chang, C. Boyle, L. J. Mawst, D. Lindberg III, T. Earles, and D. Botez, “Highly temperature insensitive, low threshold-current density (λ = 8.7–8.8 μm) quantum cascade lasers,” Appl. Phys. Lett. 106(15), 151106 (2015). [CrossRef]
14. A. Lyakh, M. Suttinger, R. Go, P. Figueiredo, and A. Todi, “5.6 μm quantum cascade lasers based on a two-material active region composition with a room temperature wall-plug efficiency exceeding 28%,” Appl. Phys. Lett. 109(12), 121109 (2016). [CrossRef]
15. D. Botez, J. C. Shin, J. D. Kirch, C.-C. Chang, L. J. Mawst, and T. Earles, “Multidimensional conduction-band engineering for maximizing the continuous-wave (CW) wallplug efficiencies of mid-infrared quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1200312 (2013) [Correction: IEEE J. Sel. Top. Quantum Electron. 19(4), 9700101 (2013)].
16. Y. T. Chiu, Y. Dikmelik, P. Q. Liu, N. L. Aung, J. B. Khurgin, and C. F. Gmachl, “Importance of interface roughness induced intersubband scattering in mid-infrared quantum cascade lasers,” Appl. Phys. Lett. 101(17), 171117 (2012). [CrossRef]
17. A. Vasanelli, A. Leuliet, C. Sirtori, A. Wade, G. Fedorov, D. Smirnov, G. Bastard, B. Vinter, M. Giovannini, and J. Faist, “Role of elastic scattering mechanisms in GaInAs/AlInAs quantum cascade lasers,” Appl. Phys. Lett. 89(17), 172120 (2006). [CrossRef]
18. D. Botez, S. Kumar, J. C. Shin, L. J. Mawst, I. Vurgaftman, and J. R. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97(7), 071101 (2010) [Erratum: Appl. Phys. Lett. 97, 199901 (2010)]. [CrossRef]
19. D. Botez, J. C. Shin, S. Kumar, J. Kirch, C.-C. Chang, L. J. Mawst, I. Vurgaftman, J. R. Meyer, A. Bismuto, B. Hinkov, and J. Faist, “The temperature dependence of key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Proc. SPIE 7953, 79530N (2011). [CrossRef]
20. Y. V. Flores, S. S. Kurlov, M. Elagin, M. P. Semtsiv, and W. T. Masselink, “S. S, Kurlov, M. Elagin, M P. Semtsiv and W.T. Masselink, “Leakage current in quantum-cascade lasers through interface roughness scattering,” Appl. Phys. Lett. 103(16), 161102 (2013). [CrossRef]
21. Y. V. Flores, “Mid-infrared quantum cascade lasers: theoretical and experimental studies on temperature driven scattering,” PhD Thesis (Humboldt-Universität zu Berlin, June 2015). https://edoc.hu-berlin.de/handle/18452/17876.
22. W. T. Masselink, M. P. Semtsiv, Y. V. Flores, S. Kurlov, M. Elagin, G. Monastyrskyi, J. F. Kischkat, and A. Aleksandrova, “J. F. and A. Aleksandrova, “AlAs/InAlAs-InGaAs QCLs grown by gas-source molecular-beam epitaxy,” Proc. SPIE 9002, 90021A (2014). [CrossRef]
23. A. Rajeev, C. Sigler, T. Earles, Y. V. Flores, L. J. Mawst, and D. Botez, “Design considerations for λ ~ 3.0–to 3.5-μm-emitting quantum cascade lasers on metamorphic buffer layers,” Opt. Eng. 57(1), 011017 (2018).
24. J. Faist, Quantum Cascade Lasers (Oxford University Press, Oxford UK, 2013), p. 114 and p.141 in Chap. 7.
25. Y. V. Flores, M. Elagin, S. S. Kurlov, G. Monastyrskyi, A. Aleksandrova, J. Kischkat, and W. T. Masselink, “Thermally activated leakage current in high performance short-wavelength quantum cascade lasers,” J. Appl. Phys. 113(13), 134506 (2013). [CrossRef]
26. D. Botez, “Comment on ‘Highly temperature insensitive quantum cascade lasers’ [Appl. Phys. Lett. 97, 251104, (2010)],” Appl. Phys. Lett. 98(21), 216101 (2011). [CrossRef]
27. J. D. Kirch and D. Botez, as per k•p analysis of the device presented in Refs. 11 and 4.
28. A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101(2), 021103 (2012). [CrossRef]
29. C. A. Wang, B. Schwarz, D. F. Siriani, M. K. Connors, L. J. Missaggia, D. R. Calawa, D. McNulty, A. Akey, M. C. Zheng, J. P. Donnelly, T. S. Mansuripur, and F. Capasso, “Sensitivity of heterointerfaces on emission wavelength of quantum cascade lasers,” J. Cryst. Growth 464, 215–220 (2017). [CrossRef]
30. C. Pflügl, L. Diehl, A. Lyakh, Q. J. Wang, R. Maulini, A. Tsekoun, C. K. Patel, X. Wang, and F. Capasso, “Activation energy study of electron transport in high performance short wavelengths quantum cascade lasers,” Opt. Express 18(2), 746–753 (2010). [CrossRef] [PubMed]
31. D. Botez, J. Kirch, C.-C. Chang, C. Boyle, H. Kim, K. Oresick, C. Sigler, L. Mawst, M. Jo, J. C. Shin, D. Gun-Kim, D. F. Lindberg, and T. L. Earles, “High internal differential efficiency, mid-infrared quantum cascade lasers,” Proc. SPIE 10123, 101230Q (2017). [CrossRef]
32. Y. Bai, N. Bandyopadhyay, S. Tsao, S. Slivken, and M. Razeghi, “Room temperature quantum cascade lasers with 27% wall plug efficiency,” Appl. Phys. Lett. 98(18), 181102 (2011). [CrossRef]
33. A. Wittmann, Y. Bonetti, J. Faist, E. Gini, and M. Giovannini, “Intersubband linewidths in quantum cascade laser designs,” Appl. Phys. Lett. 93(14), 141103 (2008). [CrossRef]
34. J. Khurgin, Y. Dikmelik, P. Liu, A. Hoffman, M. Escarra, K. Franz, and C. Gmachl, “Role of interface roughness in the transport and lasing characteristics of quantum-cascade lasers,” Appl. Phys. Lett. 94(9), 091101 (2009). [CrossRef]
35. A. Lyakh, R. Maulini, A. Tsekoun, R. Go, C. Pflugl, L. Diehl, Q. J. Wang, F. Capasso, and C. K. N. Patel, “3 W continuous wave room temperature single-facet emission from quantum cascade lasers based on nonresonant extraction design approach,” Appl. Phys. Lett. 95(14), 141113 (2009). [CrossRef]
36. A. Bismuto, R. Terazzi, M. Beck, and J. Faist, “Influence of the growth temperature on the performances of strain-balanced quantum cascade lasers,” Appl. Phys. Lett. 98(9), 091105 (2011). [CrossRef]
37. Y. T. Chiu, Y. Dikmelik, Q. Zhang, J. B. Khurgin, and C. F. Gmachl, “Engineering the intersubband lifetime with interface roughness in quantum cascade lasers,” in Conference on Lasers and Electro-Optics 2012, OSA Technical Digest Series (Optical Society of America, 2012), paper CTh3N.1. [CrossRef]
38. Giulia Pegolotti, “Quantum engineering of collective states in semiconductor nanostructures,” PhD Thesis, Univ. Paris Diderot - Paris 7, pp. 161–164 (2011).
39. T. Aellen, M. Beck, N. Hoyler, M. Giovannini, J. Faist, and E. Gini, “Doping in quantum cascade lasers. I. InAlAs – In GaAs / InP midinfrared devices,” J. Appl. Phys. 100(4), 043101 (2006). [CrossRef]
40. A. Lyakh, R. Maulini, A. Tsekoun, R. Go, and C. K. Patel, “Multiwatt long wavelength quantum cascade lasers based on high strain composition with 70% injection efficiency,” Opt. Express 20(22), 24272–24279 (2012). [CrossRef] [PubMed]
41. J. M. Wolf, “Quantum cascade laser: from 3 to 26 μm,” (Doctoral dissertation, ETH NO. 24571, Zurich, 2017).
42. A. Wittmann, A. Hugi, F. Gini, N. Hoyler, and J. Faist, “Heterogeneous high-performance quantum-cascade laser sources for broad-band tuning,” IEEE J. Quantum Electron. 44(11), 1083–1088 (2008). [CrossRef]
43. B. Schwarz, C. A. Wang, L. Missaggia, T. S. Mansuripur, P. Chevalier, M. K. Connors, D. McNulty, J. Cederberg, G. Strasser, and F. Capasso, “Watt-level continuous-wave emission from a bifunctional quantum cascade laser/detector,” ACS Photonics 4(5), 1225–1231 (2017). [CrossRef] [PubMed]
44. A. Tredicucci, F. Capasso, C. Gmachl, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “High performance interminiband quantum cascade lasers with graded superlattices,” Appl. Phys. Lett. 73(15), 2101–2103 (1998). [CrossRef]
45. C. A. Wang, B. Schwarz, D. F. Siriani, L. J. Missaggia, M. K. Connors, T. S. Mansuripur, D. R. Calawa, D. McNulty, M. Nickerson, J. P. Donnelly, K. Creedon, and F. Capasso, “MOVPE growth of LWIR AlInAs/GaInAs/InP quantum cascade lasers: Impact of growth and material quality on laser performance,” IEEE J. Sel. Top. Quantum Electron. 23(6), 1200413 (2017). [CrossRef]
46. C. A. Zmudzinski, D. Botez, and L. J. Mawst, “Simple description of laterally resonant, distributed-feedback-like modes of arrays of antiguides,” Appl. Phys. Lett. 60(2), 1049–1051 (1992). [CrossRef]
47. J. D. Kirch, C.-C. Chang, C. Boyle, L. J. Mawst, D. Lindberg III, T. Earles, and D. Botez, “5.5 W near-diffraction-limited power from resonant leaky-wave coupled phase-locked arrays of quantum cascade lasers,” Appl. Phys. Lett. 106(6), 061113 (2015). [CrossRef]
48. H. Yang, L. J. Mawst, and D. Botez, “1.6 W continuous-wave coherent power from large-index-step (Δn ≈ 0.10) near-resonant, antiguided diode laser arrays,” Appl. Phys. Lett. 76(10), 1219–1221 (2000). [CrossRef]